12 days in Czechoslovakia

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12 DAYS IN CZECHOSLOVAKIA

About the III International
Physical Olympiad for schoolchildren,
held in Brno
in June 1969,
members told
Soviet team.

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The initial acquaintance with Prague was very short. A few hours after our arrival, we were seated in the Prague-Brono train station and wished us success. True, with a small caveat: “Just don’t overtake the Czechoslovakian team!”

The day was sunny, and we spent the entire trip at the windows. Beautiful dark groves on the light green slopes of the cold gave way to blue cliffs going up - a very beautiful peaceful country. The journey was pleasant, but short. Just four hours in posed and we are in Brono.

The hosts of the Olympics tried their best to entertain their guests. On the eve of the tour, we walked up and down Brono and showed castles and other sights of the city. On the bus we gradually got to know the guys from other delegations - Poles, Romanians, Germans. We discovered that one girl came to the Olympics - a member of the Romanian room. An expectant conversation was taking place (a mixture of English and Russian).

And in the evening - the grand opening of the III International Olympiad *. The regulations for improvement are announced: there will be two rounds, the first is theoretical, the second is experimental. At the theoretical level, four problems are proposed (in mechanics, thermodynamics, electricity and optics), at the experimental level - one. Each tour lasts five hours. Problems are assessed using a full-point system. The second round takes into account the implementation of both the experimental and theoretical parts of the work. The maximum number of points that can be scored is 48. It is announced in advance how many points you need to have to get first place.

*) Schoolchildren from Bulgaria, Hungary, the GDR, Poland, Czechoslovakia and Yugoslavia took part in it.

first prize, second, third, good review. It is announced that it is mandatory to wear the badge of an Olympiad participant, since the emblem will serve as a pass to the territory of the military academy where the Olympiad will be held.

During the break, we met the Bulgarians: “We just arrived and we want to talk in Russian…” We were very, very happy about this - after all, we were pretty tired of speaking English.

The next morning, June 24th, we got up, had breakfast, ran to the hall of the military academy, concentrated… but it turned out that Zhorny had not finished translating the conditions of the problem into the languages ​​of the Olympiad participants, and everyone spent an hour looking at paintings on a plot from Greek mythology, which occupied one of the halls.

Finally, the first round is over, tomorrow is the second round, and we are looking forward to a completely free evening. But… the hosts of the Olympics felt our craving for art, and we had to go listen to Smetana’s opera “The Eaten Bride.”

Despite the lack of sleep, we completed the experimental tour successfully and went to see Austerlitz. We really liked the masterfully executed figures of “mourning matter” and “consolable bride”, standing at the entrance to the MEMORIAL HOUSE IN MEMORY OF THE AUSTRIAN AND RUSSIAN SOLDIERS who died at Austerlitz. The task has a curious action effect: if you say something quietly while standing in a corner, then nothing can be heard in the center, but everything can be clearly heard in the opposite corner. A minute later, everyone (Vedic physicists!) was pinching something in the corners.

The next morning we were taken to Bratislava. Our guides around the city were two guys - Martin and Ladiislav, who treated us sincerely in a friendly manner. We saw the Liberator Monument and Bratislava Castle. Despite the fact that the day was cloudy and gray, we still had a very bright and bright memory of Bratislava.

The next morning, the head of our delegation, Professor Yantsov, informed us that, having received three first, one second and one third first, we lost the first and second team places to the Czechoslovakians and Hungarians.

In the afternoon we explored the Punkva cave. It is difficult to describe its beauty; you need to see everything with your own eyes. There is one black stone, on which they place their hand and make a wish; according to legend, it should be used. It turned out that members of the Czech team came to the cave before the Olympics and wanted to get first place. Maybe that’s why they won?

In the evening - the closing ceremony of the Olympics. Our team received five sentences: three watches and two illustrated books. Then there was a banquet.

On June 29 we went to Prague by bus. The road was tiring, it was shaking, sometimes they woke us up and showed us castles or took us to lunch. In the evening we arrived in Prague.

After the day, we walked around the city, looked around and thought: “Oh, I’d rather go home!” It was good in Czechoslovakia, of course, but at home, as they say, it was better.

A. KLIMOV,
N. KONDRATIEV,
A. CHERNOUTSAN.

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OBJECTIVES OF THE OLYMPICS

Task 1

The system of bodies, presented on figure, is formed by three carts A, B, C, whose masses are $m_1=300$ e, $m_2=200$ e and $m_3=1500$ e, respectively.

Cart C is acted upon by a horizontal force F of such magnitude that carts A and B are at rest relative to cart C.

1. Determine: a) the tension of the insoluble thread connecting carts A and B; 6) force F.

2. Assume that cart C is stationary and determine: a) the acceleration of carts A and B; 6) threading.

When solving the problem, use air resistance, friction, moments of inertia of the block and wheels, as well as the mass of the thread.

Problem 2

A copper calorimeter, mass $m_1$, contains water of mass $m_2$ at a general temperature $t_2$. Ice is placed in the calorimeter, the mass of which is $m_3$ and the temperature is $t_3<0^\circ$ C.

a) Determine the mass of water and ice and their temperature at equilibrium for the most general values ​​of $m_1, m_2, m_3, t_2, t_3$. Write the heat transfer equations in the indicated system.

6. Determine the temperature and mass of water and ice, if up to $m_1=1,00$ ke$^*$), $m_2=1,00$ ke, $m_3=2,00$ ke, $t_2=10^\circ$ C, $t_3=-20^\circ$ C.

When solving a problem with energy losses, apply. Barometric pressure is considered normal. The specific heat of copper is $c_1=0,094$ kcal ke$^{-1}$ erad$^{-1}$, the specific heat of ice is $c_3=0,492$ kcal ke$^{-1}$ erad$^{-1}$, the specific heat of fusion of ice is $l=70,7$ kcal ke$^{-1}$.

Problem 3

A ball of mass $m$, charged with an electric charge $q$, is attached to one end

*) Two zeros after the charge indicate that the answer must be given with an accuracy of one hundredth.

conductive thread. The other end of the thread is attached to the highest point of a ring with radius $R$, which is in the vertical plane. The stake is made of rigid wire, the diameter of which can be adjusted. The charge $Q$ of the same sign as $q$ is uniformly distributed on the ring. Determine the length $l$ of the thread at which, after deflection, the ball will be on the axis of the ring, perpendicular to its plane.

Solve the problem first in general form, and then for the numerical values ​​$Q=q=9,0\cdot10^{-8}$ k, $R=5,0$ cm, $m=1,0$ e, $\varepsilon_0=8,9\cdot10^{-12}$ fm$^{-1}$. Massey threads pretenbr.

Problem 4

A polished plate is placed on top of a ground glass cube, the edge length of which is 2.00 cm, so that a thin interference layer appears in the space between it and the cube. If the plate is illuminated from above at a right angle with radiation with wavelengths from 400.0 mc to 1150 mc, for which the plate is transparent, then the condition for the maximum intensity of light reflected by the interference layer is satisfied only for two waves from the mentioned interval: for $\lambda=400,0$ mc and for another wavelength. Determine this wavelength. Calculate how much the temperature of the cube needs to be increased so that it touches the plate. The coefficient of linear thermal expansion of the stack is $\alpha=8,0\cdot10^{-6}$ erad$^{-1}$, the refractive index of air is $n=1$. The distance from the base of the cube to the plate does not change during heating.

Task 5 (experimental)

Use: two iron-nickel batteries, one dry element, one rheochord (a homogeneous wire of unknown resistance $X$, stretched along the millimeters of the scale and equipped with a sliding contact), one resistance store of value $R$, one galvanimeter (zero value for finding the scale resistance) and one hardened resistance.

Consider: a) a closed circuit consisting of two series batteries, a resistance store and an unknown resistance $X$ (reohord), 6) a series connection of a dry element and a galvanimeter with a protected resistance.

Suggest and explain such a connection of branch “b” to circuit “a”, which allows us to find such a position of motion of the rheochord $X$ in which no current flows through the galvanimeter. Create a circuit based on the diagram.

By making changes, determine: 1) the relationship between the potential difference at the terminals of two series batteries and the electromotive force of a dry cell (consider the potential difference at the terminals of both batteries constant), 2) unknown resistance $X$.

Find for what resistance $R$ the problem has a solution.